Answer:
Explanation:
Here's the long division of (2x³ + 3x² + 4x + 2) ÷ (x + 2):
2x^2 - x + 6
x + 2 | 2x^3 + 3x^2 + 4x + 2
- (2x^3 + 4x^2)
--------------
- x^2 + 4x
- (- x^2 - 2x)
-------------
6x + 2
- (6x + 12)
--------
-10
Therefore, the quotient is 2x^2 - x + 6, and the remainder is -10.
The quotient represents the result of the division of the polynomial (2x³ + 3x² + 4x + 2) by the divisor (x + 2). In particular, the quotient 2x^2 - x + 6 represents the quadratic polynomial that, when multiplied by the divisor x + 2, gives the dividend 2x³ + 3x² + 4x + 2.
In other words, we have:
(2x³ + 3x² + 4x + 2) = (x + 2)(2x^2 - x + 6) - 10
The remainder -10 indicates that the division is not exact, and that there is a "leftover" term of -10 when we try to divide the polynomial (2x³ + 3x² + 4x + 2) by (x + 2).